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Nucleation of Liquid: The solidification of metals occurs by

nucleation & growth. Same is also true for melting.

Nucleation of solid phase during freezing is much more difficult process than formation of nuclei of liquid phase during melting.

Metals do not superheat to any appreciable extent before they are liquefied, whereas some super cooling occurs almost every time a metal is frozen.

In melting most metals do not normally superheat, although superheating of the order of 0.1k has been reported for gallium.

Cont’d….

Nucleation in melting occurs on the surfaces of solids .

In this case, the nucleus , consisting of a region of the liquid phase , will be enveloped by two different surfaces .

One side is liquid-solid interface and other is gas-liquid interface.

The total surface energy of this pair of surfaces is smaller than that of a single solid-gas interface .

Γgs > Γsl + Γgl

Cont’d…. The fig(a) represents a liquid nucleus at an

early stage of development & fig(b) of the same nucleus at slightly later time.

Spreading of the liquid nucleus along the surface, in these figures, decreases the area on gas solid interface .

As a result, there is a decrease in surface energy so any rise of temperature above the equilibrium melting temperature causes a decrease in volume free energies .

Cont’d…..

It can be seen that both surface and volume free energies favor melting for even the slightest amount of super heating.

There is also another factor, diffusion rate also increases with rising temperature.

The rate of a melting reaction should therefore tend to increase with super heating.

Freezing in Alloys: Consider an isomorphous-alloy system with the

phase diagram shown in fig(a). In this system at temperature T1 , solid of composition (a) is in equilibrium with liquid of composition (b).

Let it now be assumed that fig(b) represents a volume of liquid of composition (b) placed in a long tabular mold & that heat is only removed from left end of the mold so that heat flow is linear & from right to left.

Under these conditions, freezing will start at the left end of the liquid and the small volume element (dx) may be taken to represent the first solid to form.

Cont’d……. The freezing of this volume element will take

place at temperature T1 and the composition of the solid will correspond to point (a) in fig(a)

If this layer of solid is frozen in a relatively short period of time with negligible solid-state diffusion, we can assume that it is formed from the liquid layer adjacent to the interface and not from the entire volume of the liquid.

Since the solid contains a higher ratio of A to B atoms than does the liquid layer from which it forms, the latter is depleted in A atoms and enriched in B atoms.

Cont’d….. This composition change in the liquid just

ahead of the interface increases as more solid is formed , but the increase eventually stops when a steady state condition is attained.

The change in composition of the liquid next to the interface is a similar change in the composition of the solid that can form from this layer of liquid.

Thus If the composition of the liquid correspond to point d in fig (a), than the solid that freezes must have the composition of point c.

The indicated freezing process can only occur if the temperature at interface is lowered from T1 to T2.

Cont’d….

The concentration of an excess of B atoms in the liquid adjacent to the interface reaches a maximum when when the liquid next to the solid attains the composition of point e.

At this instant the solid is able to freeze solid of composition b.when this occur, the steady state has been attained and the solid, which is formed from the liquid layer enriched in B atoms is the same as the liquid drawn into this layer.

At this time, the temperature at the interface must be T3.

Cont’d…. Notice that, In both cases, the composition of the

solid rises from its original value a to that of the original liquid b. At the interface there is also a sudden rise in composition to the value e as one passes from solid into liquid.

Following this sudden rise, the composition in the liquid decreases exponentially back to the value to the original liquid, which is b.

It is important to note that in the above discussion it is implied that there are no liquid convection currents. In the presence of such currents it is not possible to attain as large a concentration of B atoms in advance of the interface.

cont’d…. There are other factors that may also limit the

magnitude of the composition change in the liquid at the interface .

However, for our purposes we can assume that the distance composition curves shown in fig(c) are representative of what can actually happen under similar conditions during the freezing of an alloy.